Been thinking over this for a while, and have more to say. (Speaking as a polytheist and, incidentally, as a devotee of Set.)
“God of X” constructions, especially when they contain the connotation that the god in question is the force that causes X to happen, are the babytalk version of polytheism. There are a double handful of more nuanced expressions.
When gods are associated with certain things, it’s generally an indication that something about the event is taken as essentially the same as something about the god. (This is vague; I don’t know how to get it into better language.) This is a process that is constructed very similarly to metaphor or allegory (for sensible reasons; I consider myths to be, fundamentally, allegory). “Set is storming” is babytalk of much the same type as “Thunder is the angels bowling”.
But what does it mean to associate Set with storm? Perhaps (in line with the OP’s worldview) Set is the essential nature of storm, the sort of abstraction that comes of a personification and distillation of that. One can see this in one of the ways He functions in the cosmology, as a force within the order of nature that batters against the roof and finds out where it leaks.
One can no more persuade Set not to storm than one can persuade the sun not to shine or Dopers not to argue. If His nature is the nature of the storm, then that is what is; asking the storm to be something other than what it is isn’t going to be especially effective. (And in the case of the Egyptian gods in particular, that sort of self-negation is pretty much the antithesis of their worldview; self-negation is one form of the cardinal evil, personified as Apep, whose scaly ass Set beats on a regular basis.) The storm has to be dealt with on its own terms as what it is.
Another way of looking at it is that natural phenomena are seen as sharing essential essence (as opposed to being identified with the essential essence). So Set is associated with the storm because the storm looks like Set from the right angle. I think this process is much like having things in the world remind one of friends or lovers – something about that thing is akin to the experience of that person, so they are on some level symbolic of the other, at least to the individual with the association. Gods are cultural experiences; thus, they develop cultural associations.
Here the association is one of resonances and overtones; the storm has some of the same overtones as the god, or vice versa, and thus they are linked. This is probably closest to my personal worldview, for what it’s worth; I’m not actually sure, as it’s not terribly important to me.
To get something closer to the Jungian archetype form of polytheism popular among some neopagans, the god could be seen as a personification. Rather than an entity in its own right, it is the construction of a person (or culture) that makes it more possible to deal with certain things. If Set is the storm in this way of approaching things, then Set is, in some ways, a person, an anthropomorphic entity, which means the storm is no longer quite as impersonal: it is associated with a being. That being may be benevolent, malevolent, or neither; it has its own desires and agenda, and it may be that people can treat with it about its agenda in order to get desired results. The being may accept or reject those attempts; either way, it is an interaction between entities, not the machinations of something outside of thought that happens. Some people find that sort of thing soothing.
Argh. There’s more, and I am so not figuring out how to get it into language.